Generalized shuffle-exchange digraphs: Hamiltonian properties

Hongfang Liu, D. Frank Hsu, Susumu Horiguchi

Research output: Contribution to journalConference article

1 Scopus citations

Abstract

The k-ary n-dimensional shuffle-exchange directed network S(k, n) consists of kn nodes such that each node is represented as an k-ary n-tuple vector, a1a2···an, where ai is in [0, k-1]. Node a1a2···an is adjacent to node a2a3···ana1 (one shuffle link) and k-1 other nodes a1a2···an-1b, where b∈[0, k-1] and b≠an (k-1 exchange links). S(k, n) have been widely used as topologies for VLSI networks, parallel architectures, and communication systems. However, since S(k, n) does not exist for the number of nodes between kn and kn+1, Liu and Hsu have recently proposed a class of digraphs GS(k, N), which generalized S(k, n) to any number N of nodes. They also showed that GS(k, N) retains all the nice properties of S(k, n). In this paper, we survey these combinatorial properties and study Hamiltonian properties of GS(k, N). In particular, we have successfully obtained Hamiltonian circuit for GS(k, k(k+1)) for any k>2.

Original languageEnglish (US)
Pages (from-to)VI-157-VI-160
JournalProceedings - IEEE International Symposium on Circuits and Systems
Volume6
StatePublished - Jan 1 1999
EventProceedings of the 1999 IEEE International Symposium on Circuits and Systems, ISCAS '99 - Orlando, FL, USA
Duration: May 30 1999Jun 2 1999

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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